Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-13T09:25:08.838Z Has data issue: false hasContentIssue false
  • English
  • Français

THE CLASSIFICATION OF SOME MODULAR FROBENIUS GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  25 July 2011

JUANJUAN FAN ,
NI DU  and
JIWEN ZENG
JUANJUAN FAN
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, PR China (email: maygaxm@hotmail.com)
NI DU*
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, PR China (email: duni@xmu.edu.cn)
JIWEN ZENG
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, PR China (email: jwzeng@xmu.edu.cn)
*
✉For correspondence; e-mail: duni@xmu.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Fix a prime number p. Let G be a p-modular Frobenius group with kernel N which is the minimal normal subgroup of G. We give the complete classification of G when N has three, four or five p-regular conjugacy classes. We also determine the structure of G when N has more than five p-regular conjugacy classes.

Keywords

modular Frobenius groupsminimal normal subgroupsp-regular conjugacy classes

MSC classification

Secondary: 20C20: Modular representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 11 - 18
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This research was supported by the Fundamental Research Funds for the Central Universities (No. 2010121003).

References

[1]Alemany, E., Beltrán, A. and Felipe, M. J., ‘Finite groups with two p-regular conjugacy class lengths II’, Bull. Aust. Math. Soc. 79 (2009), 419–425.CrossRefGoogle Scholar
[2]Dixon, J. D. and Mortimer, B., Permutation Groups (Springer, New York, 1996).CrossRefGoogle Scholar
[3]Gallagher, P. X., ‘The number of conjugacy classes in a finite group’, Math. Z. 118 (1970), 175–179.CrossRefGoogle Scholar
[4] The GAP Group, ‘GAP – Groups, Algorithms, and Programming’, Version 4.4, 2006, http://www.gap-system.org.Google Scholar
[5]Isaacs, I. M., ‘Lifting Brauer characters of p-solvable groups’, Pacific J. Math. 53 (1974), 171–188.CrossRefGoogle Scholar
[6]Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).Google Scholar
[7]Kuisch, E. B. and van der Waall, R. W., ‘Modular Frobenius groups’, Manuscripta Math. 90 (1996), 403–427.CrossRefGoogle Scholar
[8]Kurzweil, H. and Stellmacher, B., The Theory of Finite Groups: An Introduction (Springer, New York, 2004).CrossRefGoogle Scholar
[9]Navarro, G., Characters and Blocks of Finite Groups (Cambridge University Press, Cambridge, 1978).Google Scholar
[10]Robinson, D. J. S., A Course in the Theory of Groups (Springer, New York, Berlin, 2003).Google Scholar